A362798 E.g.f. satisfies A(x) = 1/(1-x)^(A(x)^(x^2)).

1, 1, 2, 6, 48, 360, 2820, 31500, 393568, 5111568, 78491520, 1345893120, 24286008384, 483716087712, 10526811186528, 241867328844960, 5957816820215040, 157412355684364800, 4380674530640290560, 128826276098289179904, 4010282529115722232320

Offset: 0

Author

Seiichi Manyama, May 04 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A052813, A362796.

Cf. A362795, A362800.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(-lambertw(x^2*log(1-x)))))

Formula

E.g.f.: exp( -LambertW(x^2 * log(1-x)) / x^2 ) = 1/(1-x)^exp( -LambertW(x^2 * log(1-x)) ).

E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * (-log(1-x))^k / k!.